The perimeter of a circle is called the circumference of a circle.

But it is not easy to find the circumference of a circle because the boundary is not made of straight lines or edges. This problem of calculating the circumference of a circle has puzzled mathematicians for centuries. It was known in ancient Egypt that the distance around the boundary of a circle was directly linked to the length of its diameter.

This relationship, expressed as

results in a number (called * pi*) with a value of

= 3.141 592 653 589 793 238 462 643 383 279 ….

This number continues forever without repetition and does not have a pattern that repeats. It is important to note that is an * irrational number* as it does not have an exact fraction or decimal value.

Over the centuries, many people have tried to express as a fraction. In ancient Egypt (around 1700 BC), ~ 3.1605 was used to estimate . In ancient Greece, the great mathematician Archimedes (around 225 BC) stated that the value of lay between 3 and 3. The famous Chinese mathematician Tsu Ch’ung-chih (circa 470 AD) gave the value of as , which is accurate to 6 decimal places. In the 13th century, Fibonacci estimate the value as ~ 3.14 8…

However, today the commonly used approximations for is as a fraction, and 3.14 as a decimal.

If you are using a scientific calculator, the value of should be obtained by pressing the key, unless otherwise indicated.

is used in most calculations involving circles and cylinders.

## Formula for circumference of a circle

As discussed above,

Rearranging this, we get the formula for circumference C =

In other words, the circumference of a circle is obtained by multiplying and the diameter (d) of the circle.

This formula can be expressed in terms of the radius, r as:

C =

= (since d = 2r)

=

C = | C = |

Now let us look at a few examples:

1. What is the circumference of this circle?

C =

=

= 44 cm

2. Calculate the circumference of the circle, correct to 1 decimal place.

C =

=

=

= 56.5 cm

**Note**: In this example, the circumference could also be expressed as

We’ll look at calculating the area of a circle.